On Some Aspects of Oscillation Theory and Geometry

Released on by Bruno Bianchini
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  • On Some Aspects of Oscillation Theory and Geometry Book Detail

  • Author : Bruno Bianchini
  • Release Date : 2013-08-23
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 208
  • ISBN 13 : 0821887998
  • File Size : 3,3 MB
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On Some Aspects of Oscillation Theory and Geometry by Bruno Bianchini PDF Summary

Book Description: The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.

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